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Guerrilla Tactics for the GRE™*:

Secrets and Strategies the Test Writers

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Guerrilla Tactics for the GRE

Sample 1: Table of Contents
Sample 2: Vocabulary Tips for the GRE
Sample 3: Rates and Distances
Sample 4: Lie vs. Lay

Math Word Problems for the GRE

Sample 1: Table of Contents
Sample 2: Interest on Financial Products
Sample 3: Sample Problems with Statistics
Sample 4: Problems with All Variables

Guerrilla Review for the GRE

Table of Contents
Sample Section: Verbal 9
Sample Section: Answer Key for Verbal 9

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Two Sample Problems: Rates and Distances

The GRE often includes at least one word problem that uses the rate formula: Distance = Rate X Time. The underlying concept is simple, as illustrated by the following example:

If Joe drives at an average speed of 70 miles per hour, how long will it take him to travel 560 miles?

Since Distance = Rate x Time, Time = Distance/Rate = (560 miles/70miles per hour) = 8 hours

Unfortunately, the GRE rarely tests these concepts in such a straightforward manner. Instead, it includes pesky problems in which you must apply your knowledge of the rate equation to some fairly contrived situations, with multiple vehicles that are moving at different speeds (and for different amounts of time).

Example 1: Two Trains on Opposite Tracks - Finding the Time

Train A and Train B left the Kansas City Station at the same time and travelled in opposite directions. If Train A travelled at an average rate of 115 miles per hour and Train B travelled at an average rate of 85 miles per hour, how many hours will it take Train A and Train B to be 1,800 miles apart?

Solution: The first step for this type of problem is to draw a quick chart of what we know.

In this case, we will let x = the time it takes for Train A and Train B to travel 1,800 miles.

We can also enter the rates for each train and write an expression for their respective distances. Next, we must use this information to solve for x.

Train A and Train B each travelled a portion of the total distance, which is 1,800 miles. Our equation, therefore, is:

Train A's Distance + Train B's Distance = Total Distance
115 x + 85X = 1,800
200x = 1800
X = 9 hours Choice D is correct

Example 2: Finding the Average Rate

On Valentine's Day, a busy florist drove his delivery truck from Palm Beach to Miami at an average rate of 45 miles per hour. On his return trip to Palm Beach, he encountered rush hour traffic, which slowed him to an average speed of 25 miles per hour. What was the driver's average speed for the trip, in miles per hour?

Solution: As you probably suspect, the seemingly obvious answer of 35 mph, which is choice c, is incorrect. When cars travel at different speeds, they take different lengths of time to cover the same distance. Consequently, you cannot simply average the two speeds to get the correct answer. Instead, you must use the following formula to determine the average rate:

Average Rate = Total Distance / Total Time

In this case, the test writers did not give us any specific numbers, so we are free to pick any value for the total distance. In this case, we will use 100 miles for the total distance, which makes each leg of the trip (the distance from Palm Beach to Miami) equal to one-half of 100, or 50 miles.

For the trip from Palm Beach to Miami,
Average Rate = 50 miles/ 45 miles per hour = 1.11 hours

For the return trip from Miami to Palm Beach,
Average rate = 50 miles / 25 miles per hour = 2 hours

Hence, the total time was 3.11 hours

Going back to the original equation, for the total trip,

Average Rate = Total Distance / Total Time = 100 miles/3.11 hours = 32 miles per hour

The correct answer choice is b.

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